Representation of hyperfunction solutions in a hypo-analytic structure
type: Item
instance of: scholarly article
title: Representation of hyperfunction solutions in a hypo-analytic structure
zbMATH Open document ID: 0959.35031
published in: Mathematische Zeitschrift
publication date: 2001-04-26T00:00:00Z
review text: In this paper, the author analyzed the local structure of the hyperfunction solutions in a hypo-analytic manifold. Such class of solutions, which generalizes both the notion of (distribution) solutions to systems of vector fields associated to locally integrable structure and of hyperfunctions defined in a maximally real submanifold of the complex space. By using the FBI transform, the author got an elementary proof of the expected regularity for the solutions of an operator in the Kaneko's class acting on a maximally real submanifold of the complex space, and proved a result on representation of hyperfunction solutions on hypo-analytic structure which is a generalization of a former result due to Baouendi-Treves in the classical set-up, and furthermore proved that in a hypercomplex structure all hyperfunction solutions are necessarily hypo-analytic. Finally, the author extended further the results to cohomology classes of the differential complex naturally associated to a given hypo-analytic structure.
reviewed by: Zeng Yuesheng
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 46F15
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 1463419
zbMATH Keywords: hypo-analytic manifold
zbMATH Keywords: hypercomplex structure
zbMATH Keywords: cohomology classes
author: Paulo D. Cordaro
MaRDI profile type: Publication
full work available at URL: s002090050491
OpenAlex ID: W2074726598
DOI: 10.1007/S002090050491
description: scientific article; zbMATH DE number 1463419